{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SDE - Heston model\n",
    "\n",
    "## Contents\n",
    "   - [Correlated Normal random variables](#sec1)\n",
    "   - [Heston model](#sec2)\n",
    "      - [Distribution of log-returns](#sec2.1)\n",
    "   - [Characteristic function](#sec3)\n",
    "      - [Option pricing](#sec3.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as scp\n",
    "import scipy.stats as ss\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.special as scps\n",
    "from statsmodels.graphics.gofplots import qqplot\n",
    "from scipy.linalg import cholesky\n",
    "from functools import partial\n",
    "from functions.probabilities import Heston_pdf, Q1, Q2\n",
    "from functions.cython.cython_Heston import Heston_paths_log, Heston_paths\n",
    "from scipy.optimize import minimize\n",
    "\n",
    "from IPython.display import display\n",
    "import sympy; sympy.init_printing()\n",
    "\n",
    "def display_matrix(m):\n",
    "    display(sympy.Matrix(m))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec1'></a>\n",
    "# Correlated Normal random variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to generate $n$ correlated Gaussian distributed random variables\n",
    "\n",
    "$$ Y \\sim \\mathcal{N}(\\mu, \\Sigma) $$\n",
    "\n",
    "where $Y=(𝑌_1,...,𝑌_n)$ is the vector to simulate, $\\mu = (\\mu_1,...,\\mu_n)$ the vector of means and $\\Sigma$\n",
    "the [covariance matrix](https://en.wikipedia.org/wiki/Covariance_matrix),\n",
    "\n",
    "1) we first need to simulate a vector of uncorrelated standard Normal random variables, $Z$\n",
    "\n",
    "2) then find a square root of $\\Sigma$, i.e. a matrix $C$ such that $C C^T = \\Sigma$.\n",
    "\n",
    "The vector is given by $$Y = \\mu + C Z .$$ \n",
    "\n",
    "A popular choice to calculate $C$ is the [Cholesky decomposition](https://en.wikipedia.org/wiki/Cholesky_decomposition).\n",
    "\n",
    "#### Example:\n",
    "\n",
    "Let us consider the following 2-dimensional covariance matrix:\n",
    "\n",
    "$$ \\Sigma = \\left(\n",
    "\\begin{array}{cc}\n",
    "1    & \\rho   \\\\\n",
    "\\rho & 1      \\\\\n",
    "\\end{array}\n",
    "\\right) $$\n",
    "\n",
    "where for simplicity I chose $Var[Y_1]=Var[Y_2]=1$, such that $\\Sigma$ corresponds to the [correlation matrix](https://en.wikipedia.org/wiki/Correlation_and_dependence#Correlation_matrices).  I also set $\\mu = 0$.\n",
    "\n",
    "In python we can use the built in function `scipy.stats.multivariate_normal` as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "COV: \n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0 & 0.6\\\\0.6 & 1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1.0  0.6⎤\n",
       "⎢        ⎥\n",
       "⎣0.6  1.0⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "correlation matrix: \n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0 & 0.6\\\\0.6 & 1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1.0  0.6⎤\n",
       "⎢        ⎥\n",
       "⎣0.6  1.0⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "SIZE = 1000000\n",
    "rho = 0.6\n",
    "\n",
    "MU = np.array([0, 0])\n",
    "COV = np.array( [[1, rho], [rho, 1]] ); \n",
    "print(\"COV: \"); display_matrix(COV)\n",
    "\n",
    "Y = ss.multivariate_normal.rvs( mean=MU, cov=COV, size=SIZE )\n",
    "\n",
    "print(\"correlation matrix: \"); display_matrix(np.corrcoef(Y.T).round(2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we want to use the algorithm proposed above, we have to find the matrix C.\n",
    "\n",
    "In two dimensions it has the simple form:\n",
    "\n",
    "$$ C = \\left(\n",
    "\\begin{array}{cc}\n",
    "1    & 0   \\\\\n",
    "\\rho & \\sqrt{1-\\rho^2}  \\\\\n",
    "\\end{array}\n",
    "\\right). $$\n",
    "\n",
    "By a simple matrix multiplication we can verify that:\n",
    "\n",
    "$$ \\left(\n",
    "\\begin{array}{cc}\n",
    "1    & 0   \\\\\n",
    "\\rho & \\sqrt{1-\\rho^2}  \\\\\n",
    "\\end{array}\n",
    "\\right) \\cdot \n",
    "\\left(\n",
    "\\begin{array}{cc}\n",
    "1    & \\rho  \\\\\n",
    "0 & \\sqrt{1-\\rho^2}  \\\\\n",
    "\\end{array}\n",
    "\\right)\n",
    "= \\left(\n",
    "\\begin{array}{cc}\n",
    "1    & \\rho   \\\\\n",
    "\\rho & 1      \\\\\n",
    "\\end{array}\n",
    "\\right)\n",
    "$$\n",
    "\n",
    "Therefore, in 2 dimensions there is no need to use the Cholesky decomposition. We simply have:\n",
    "\n",
    "$$ \\begin{cases} Y_1 = Z_1 \\\\ Y_2 = \\rho Z_1 + \\sqrt{1-\\rho^2} Z_2  \\end{cases} $$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "correlation matrix: \n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0 & 0.6\\\\0.6 & 1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1.0  0.6⎤\n",
       "⎢        ⎥\n",
       "⎣0.6  1.0⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Y_1 = np.random.normal(loc=0, scale=1, size=SIZE )\n",
    "Y_2 = rho * Y_1 + np.sqrt(1-rho**2) * np.random.normal(loc=0, scale=1, size=SIZE )\n",
    "print(\"correlation matrix: \"); display_matrix(np.corrcoef(Y_1,Y_2).round(2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For higher dimensional problems, the function `scipy.linalg.cholesky` [doc](https://docs.scipy.org/doc/scipy-0.16.1/reference/generated/scipy.linalg.cholesky.html) can help:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cholesky: \n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0 & 0.6\\\\0.0 & 0.8\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1.0  0.6⎤\n",
       "⎢        ⎥\n",
       "⎣0.0  0.8⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation matrix: \n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0 & 0.6\\\\0.6 & 1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "⎡1.0  0.6⎤\n",
       "⎢        ⎥\n",
       "⎣0.6  1.0⎦"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Cholesky: \"); display_matrix( cholesky(COV) )\n",
    "print(\"Correlation matrix: \"); display_matrix( cholesky(COV, lower=True) @ cholesky(COV) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec2'></a>\n",
    "# Heston model\n",
    "\n",
    "The [Heston process](https://en.wikipedia.org/wiki/Heston_model) is described by the SDE: \n",
    "\n",
    "$$ \\begin{cases}\n",
    "dS_t = \\mu S_t dt + \\sqrt{v_t} S_t dW^1_t \\\\\n",
    "dv_t = \\kappa (\\theta - v_t) dt + \\sigma \\sqrt{v_t} dW^2_t \n",
    "\\end{cases}$$\n",
    "\n",
    "The stock price follows a \"geometric Brownian motion\" with a stochastic volatility. The square of the volatility (the variance) follows a CIR process.     \n",
    "Have a look at the notebook **1.2** for more information on the CIR process.\n",
    "\n",
    "The parameters are:\n",
    "- $\\mu$ drift of the stock process\n",
    "- $\\kappa$ mean reversion coefficient of the variance process\n",
    "- $\\theta$ long term mean of the variance process \n",
    "- $\\sigma$  volatility coefficient of the variance process\n",
    "- $\\rho$ correlation between $W^1$ and $W^2$ i.e.\n",
    "$$ dW^1_t dW^2_t = \\rho dt $$\n",
    "\n",
    "We will also require that $2\\kappa \\theta > \\sigma^2$ (Feller condition)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Path generation\n",
    "\n",
    "The Heston process can be discretized using the Euler-Maruyama method proposed in the notebook **2.1**.\n",
    "\n",
    "In the next cell I present the algorithm that produces sample paths of the Heston process. In this example, I prefer to use the log-variables $X_t = \\log(S_t)$ and $Y_t = \\log(v_t)$ in order to avoid negative values for the process $\\{v_t\\}_{t\\geq 0}$.    \n",
    "\n",
    "$$ \\begin{cases}\n",
    "dX_t = \\biggl( \\mu - \\frac{1}{2} e^{Y_t} \\biggr) dt + e^{Y_t/2} dW^1_t \\\\\n",
    "dY_t = e^{-Y_t} \\biggl[ \\kappa (\\theta - e^{Y_t}) - \\frac{1}{2}\\sigma^2 \\biggr] dt + \\sigma e^{-Y_t/2} dW^2_t \n",
    "\\end{cases}$$\n",
    "\n",
    "This is an arbitrary choice! \n",
    "\n",
    "**Comment:**         \n",
    "From a theoretical point of view, using log-variables is the best choice, because it avoids negative values without any tweak of the original process.     \n",
    "From the practical point of view, it is better not to use log-variables!    \n",
    "The reason is that the algorithm can produce NaNs or overflows when the time steps are not small enough (e.g. for $N<20000$). This happens quite frequently. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 36 s, sys: 284 ms, total: 36.3 s\n",
      "Wall time: 36 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "np.random.seed(seed=42) \n",
    "\n",
    "N = 1000000             # time steps \n",
    "paths = 3               # number of paths\n",
    "T = 1\n",
    "T_vec, dt = np.linspace(0,T,N, retstep=True )\n",
    "dt_sq = np.sqrt(dt)\n",
    "\n",
    "S0 = 100          # spot price\n",
    "X0 = np.log(S0)   # log price\n",
    "v0 = 0.04         # spot variance\n",
    "Y0 = np.log(v0)   # log-variance \n",
    "\n",
    "mu = 0.1                                           # drift\n",
    "rho = -0.2                                         # correlation coefficient\n",
    "kappa = 2                                          # mean reversion coefficient\n",
    "theta = 0.04                                       # long-term variance\n",
    "sigma = 0.3                                        # Vol of Vol - Volatility of instantaneous variance\n",
    "std_asy = np.sqrt( theta * sigma**2 /(2*kappa) )   # asymptotic standard deviation for the CIR process\n",
    "assert(2*kappa * theta > sigma**2)                 # Feller condition\n",
    "\n",
    "# Generate random Brownian Motion\n",
    "MU = np.array([0, 0])\n",
    "COV = np.matrix([[1, rho], [rho, 1]])\n",
    "W = ss.multivariate_normal.rvs( mean=MU, cov=COV, size=(paths,N-1) )\n",
    "W_S = W[:,:,0]   # Stock Brownian motion:     W_1\n",
    "W_v = W[:,:,1]   # Variance Brownian motion:  W_2\n",
    "\n",
    "# Initialize vectors\n",
    "Y = np.zeros((paths,N))\n",
    "Y[:,0] = Y0\n",
    "X = np.zeros((paths,N))\n",
    "X[:,0] = X0\n",
    "v = np.zeros(N)\n",
    "\n",
    "# Generate paths\n",
    "for t in range(0,N-1):\n",
    "    v = np.exp(Y[:,t])    # variance \n",
    "    v_sq = np.sqrt(v)     # square root of variance \n",
    "    \n",
    "    Y[:,t+1] = Y[:,t] + (1/v)*( kappa*(theta - v) - 0.5*sigma**2 )*dt + sigma * (1/v_sq) * dt_sq * W_v[:,t]   \n",
    "    X[:,t+1] = X[:,t] + (mu - 0.5*v)*dt + v_sq * dt_sq * W_S[:,t]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,5))\n",
    "ax1 = fig.add_subplot(121); ax2 = fig.add_subplot(122)\n",
    "\n",
    "ax1.plot(T_vec, np.exp(X.T) )\n",
    "ax1.set_title(\"Heston model, Stock process. 3 paths\"); ax1.set_xlabel(\"Time\"); ax1.set_ylabel(\"Stock\")\n",
    "ax2.plot(T_vec, np.exp(Y.T) )\n",
    "ax2.set_title(\"Heston model, Variance process. 3 paths\"); ax2.set_xlabel(\"Time\"); ax2.set_ylabel(\"Variance\")\n",
    "ax2.plot(T_vec, (theta + std_asy)*np.ones_like(T_vec), label=\"1 asymptotic std dev\", color=\"black\" )\n",
    "ax2.plot(T_vec, (theta - std_asy)*np.ones_like(T_vec), color=\"black\" )\n",
    "ax2.plot(T_vec, theta*np.ones_like(T_vec), label=\"Long term mean\" )\n",
    "ax2.legend(loc=\"upper right\"); \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec2.1'></a>\n",
    "# Distribution of log-returns\n",
    "\n",
    "The python code presented above is very slow when we want to generate a big number of paths.    \n",
    "For this reason I implemented it in Cython. \n",
    "\n",
    "For a short introduction to Cython, have a look at the notebook **A2**.     \n",
    "This is the [Cython code](./functions/cython/cython_Heston.pyx), that makes also use of some C functions.\n",
    "\n",
    "\n",
    "##### CYTHON implementation\n",
    "\n",
    "1) The function `Heston_paths_log` contains the code presented above, but translated in Cython.      \n",
    "   The code returns only the \"good\" paths. It means that if there are overflows, they are ignored.     \n",
    "   Since this method returns a \"random\" number of paths, I will prefer to use the next method.\n",
    "\n",
    "2) The function `Heston_paths` implements the discretization of the original process $(S_t,v_t)_{t\\geq 0}$.\n",
    "   The CIR process is discretized using the method (4) presented in the notebook **1.2** i.e. by taking the absolute value of the variance at each time step.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I import the following cython functions:\n",
    "```python\n",
    "from functions.cython.cython_Heston import Heston_paths_log, Heston_paths\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us re-define the parameters of the process, together with the parameters of the CIR density."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu = 0.1                                           # drift\n",
    "rho = -0.9                                         # correlation coefficient\n",
    "kappa = 2                                          # mean reversion coefficient\n",
    "theta = 0.04                                       # long-term mean of the variance\n",
    "sigma = 0.3                                        # (Vol of Vol) - Volatility of instantaneous variance\n",
    "T = 1                                              # Terminal time\n",
    "v0 = 0.04                                          # spot variance\n",
    "S0 = 100                                           # spot stock price \n",
    "\n",
    "c = 2*kappa / ((1-np.exp(-kappa*T))*sigma**2)\n",
    "df = 4*kappa*theta / sigma**2                      # degrees of freedom\n",
    "nc = 2*c*v0*np.exp(-kappa*T)                       # non-centrality parameter "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next cell just wants to check if there are overflows for small value of $N$ (big time steps)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING.  10  paths have been removed because of the overflow.\n",
      "SOLUTION: Use a bigger value N.\n"
     ]
    }
   ],
   "source": [
    "_,_ = Heston_paths_log(N=500, paths=20000, T=T, S0=S0, v0=v0, \n",
    "                  mu=mu, rho=rho, kappa=kappa, theta=theta, sigma=sigma  )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "OK.... now we are going to use the other function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 38.1 s, sys: 0 ns, total: 38.1 s\n",
      "Wall time: 38.1 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "S,V = Heston_paths(N=20000, paths=20000, T=T, S0=S0, v0=v0, \n",
    "                  mu=mu, rho=rho, kappa=kappa, theta=theta, sigma=sigma  )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "log_R = np.log(S/S0)\n",
    "x = np.linspace(log_R.min(), log_R.max(), 500)\n",
    "y = np.linspace(0.00001, 0.3, 500)\n",
    "\n",
    "fig = plt.figure(figsize=(16,5))\n",
    "ax1 = fig.add_subplot(121); ax2 = fig.add_subplot(122)\n",
    "\n",
    "ax1.plot(y, ss.ncx2.pdf(y, df, nc, scale=1/(2*c)), color=\"green\", label=\"non-central-chi-squared\")\n",
    "ax1.hist(V, density=True, bins=100, facecolor=\"LightBlue\", label=\"frequencies of v_T\")\n",
    "ax1.legend(); ax1.set_title(\"Histogram vs CIR distribution\"); ax1.set_xlabel(\"v_T\")\n",
    "\n",
    "ax2.plot(x, ss.norm.pdf(x, log_R.mean(), log_R.std(ddof=0)), color='r', label=\"Normal density\")\n",
    "ax2.hist(log_R, density=True, bins=100, facecolor=\"LightBlue\", label=\"frequencies of log-returns\")\n",
    "ax2.legend(); ax2.set_title(\"Histogram vs log-returns distribution\"); ax2.set_xlabel(\"log(S_T/S0)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "qqplot(log_R, line='s');  plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The distribution of the log-returns is far from being normal!!**    \n",
    "(as you can see also from the q-q plot)\n",
    "\n",
    "This is a good property, because we can describe better the features of the empirical distributions obtained from market data!\n",
    "\n",
    "You can play with the correlation parameter $\\rho$ in order to obtain different skewness values.\n",
    "\n",
    "- For negative $\\rho$, we generate a log-return distribution with negative skewness.\n",
    "- For positive $\\rho$, we generate a log-return distribution with positive skewness."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 39 s, sys: 0 ns, total: 39 s\n",
      "Wall time: 39 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "S2,_ = Heston_paths(N=20000, paths=20000, T=T, S0=S0, v0=v0, \n",
    "                  mu=mu, rho=0.9, kappa=kappa, theta=theta, sigma=sigma  )\n",
    "log_R2 = np.log(S2/S0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-1, 1, 70)\n",
    "\n",
    "fig = plt.figure(figsize=(16,5))\n",
    "ax1 = fig.add_subplot(121); ax2 = fig.add_subplot(122)\n",
    "\n",
    "ax1.plot(x, [Heston_pdf(i, t=T, v0=v0, mu=mu, theta=theta, sigma=sigma, kappa=kappa, rho=0.9) for i in x], \n",
    "       color='blue', label=\"Heston density\" )\n",
    "ax1.plot(x, ss.norm.pdf(x, log_R2.mean(), log_R2.std(ddof=0)), color='r', label=\"Normal density\")\n",
    "ax1.hist(log_R2, density=True, bins=100, facecolor=\"LightBlue\", label=\"frequencies of R_T\")\n",
    "ax1.legend(); ax1.set_title(\"Histogram vs log-returns, Positive skew\"); ax1.set_xlabel(\"log(S_T/S0)\")\n",
    "\n",
    "ax2.plot(x, [Heston_pdf(i, t=T, v0=v0, mu=mu, theta=theta, sigma=sigma, kappa=kappa, rho=-0.9) for i in x], \n",
    "       color='blue', label=\"Heston density\" )\n",
    "ax2.plot(x, ss.norm.pdf(x, log_R.mean(), log_R.std(ddof=0)), color='r', label=\"Normal density\")\n",
    "ax2.hist(log_R, density=True, bins=100, facecolor=\"LightBlue\", label=\"frequencies of R_T\")\n",
    "ax2.legend(loc=\"upper left\") \n",
    "ax2.set_title(\"Histogram vs log-returns, Negative skew\"); ax2.set_xlabel(\"log(S_T/S0)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The skewness for rho= -0.9 is:  -1.1755429109760809\n",
      "The skewness for rho= +0.9 is:  1.2052441928707955\n"
     ]
    }
   ],
   "source": [
    "print(\"The skewness for rho= -0.9 is: \", ss.skew(log_R) )\n",
    "print(\"The skewness for rho= +0.9 is: \", ss.skew(log_R2) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the pictures above we can see the difference between the Normal distribution and the Heston distribution!\n",
    "\n",
    "I used the function `Heston_pdf`, which implements the Fourier inversion of the Heston characteristic function using the Gil-Pelaez formula.     \n",
    "\n",
    "For more information on Fourier inversion see the notebook **1.3**. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec3'></a>\n",
    "# Characteristic function\n",
    "\n",
    "The characteristic function (CF) for the Heston model was presented for the first time in the original paper of Heston (1993) [1].    \n",
    "\n",
    "The Heston CF is very useful for the computation of option prices. All the other methods, such as Monte Carlo or PDE, are quite slow, while Fourier inversion (as we have seen in the notebook **1.3**) is super fast!\n",
    "\n",
    "##### Issue with the Heston CF\n",
    "\n",
    "The Heston CF works well for short time $T$.    \n",
    "However, when the time increases this CF exhibits discontinuities due to the multivalued complex functions (the complex square root and the complex logarithm need to have a specified [Principal brach](https://en.wikipedia.org/wiki/Principal_branch)).\n",
    "A consequence is that the numerical integration becomes unstable.\n",
    "\n",
    "In the important articles [2] and [3], different (but equivalent) forms of the Heston CF are presented. These CFs consider different [Riemann surfaces](https://en.wikipedia.org/wiki/Riemann_surface) and resolve the problem.\n",
    "\n",
    "In the following I will show how the CF proposed by Schoutens (in [2]) performs better than the Heston CF.     \n",
    "In these notebooks, all the functions that consider the Heston CF are implemented using the CF `cf_Heston_good` proposed by Schoutens."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = 0.05                                           # drift\n",
    "rho = -0.8                                         # correlation coefficient\n",
    "kappa = 3                                          # mean reversion coefficient\n",
    "theta = 0.1                                        # long-term mean of the variance\n",
    "sigma = 0.25                                       # (Vol of Vol) - Volatility of instantaneous variance\n",
    "T = 15                                             # Terminal time\n",
    "K = 100                                            # Stike  \n",
    "v0 = 0.08                                          # spot variance\n",
    "S0 = 100                                           # spot stock price \n",
    "k = np.log(K/S0)                                   # log moneyness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cf_Heston(u, t, v0, mu, kappa, theta, sigma):\n",
    "    \"\"\"\n",
    "    Heston characteristic function as proposed in the original paper of Heston (1993)\n",
    "    \"\"\"\n",
    "    xi = kappa - sigma*rho*u*1j\n",
    "    d = np.sqrt( xi**2 + sigma**2 * (u**2 + 1j*u) )\n",
    "    g1 = (xi+d)/(xi-d)\n",
    "    cf = np.exp( 1j*u*mu*t + (kappa*theta)/(sigma**2) * ( (xi+d)*t - 2*np.log( (1-g1*np.exp(d*t))/(1-g1) ))\\\n",
    "              + (v0/sigma**2)*(xi+d) * (1-np.exp(d*t))/(1-g1*np.exp(d*t)) )\n",
    "    return cf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cf_Heston_good(u, t, v0, mu, kappa, theta, sigma):\n",
    "    \"\"\"\n",
    "    Heston characteristic function as proposed by Schoutens (2004)\n",
    "    \"\"\"\n",
    "    xi = kappa - sigma*rho*u*1j\n",
    "    d = np.sqrt( xi**2 + sigma**2 * (u**2 + 1j*u) )\n",
    "    g1 = (xi+d)/(xi-d)\n",
    "    g2 = 1/g1\n",
    "    cf = np.exp( 1j*u*mu*t + (kappa*theta)/(sigma**2) * ( (xi-d)*t - 2*np.log( (1-g2*np.exp(-d*t))/(1-g2) ))\\\n",
    "              + (v0/sigma**2)*(xi-d) * (1-np.exp(-d*t))/(1-g2*np.exp(-d*t)) )\n",
    "    return cf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "cf_H_b = partial(cf_Heston, t=T, v0=v0, mu=r, theta=theta, sigma=sigma, kappa=kappa ) \n",
    "cf_H_b_good = partial(cf_Heston_good, t=T, v0=v0, mu=r, theta=theta, sigma=sigma, kappa=kappa ) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = np.linspace(-4,4, 100)\n",
    "\n",
    "plt.figure(figsize=(12,5))\n",
    "plt.plot(u, np.real(cf_H_b(u)), label=\"Heston CF\" )\n",
    "plt.plot(u, np.real(cf_H_b_good(u)), label=\"Schoutens CF\" )\n",
    "plt.title(\"Comparison of stable and instable Heston characteristic functions\")\n",
    "plt.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='sec3.1'></a>\n",
    "## Option pricing\n",
    "\n",
    "We can compare the values of an European call option computed with the following two pricing methods: \n",
    "\n",
    "(as usual we consider the parameters defined above as the *risk neutral* parameters)\n",
    "\n",
    "##### Monte Carlo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Heston Monte Carlo call price:  64.91651203382668\n",
      "With standard error:  1.1653997059829462\n",
      "-----------------------------------\n",
      "CPU times: user 40.6 s, sys: 0 ns, total: 40.6 s\n",
      "Wall time: 40.6 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "S,v = Heston_paths(N=20000, paths=20000, T=T, S0=S0, v0=v0, mu=r, rho=rho, kappa=kappa, theta=theta, sigma=sigma  )\n",
    "DiscountedPayoff = np.exp(-r*T) * np.maximum(S-K,0) \n",
    "V = scp.mean( DiscountedPayoff )\n",
    "std_err = ss.sem( DiscountedPayoff )\n",
    "print(\"Heston Monte Carlo call price: \", V)\n",
    "print(\"With standard error: \", std_err)\n",
    "print(\"-----------------------------------\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Fourier inversion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Heston Fourier inversion call price:  65.27786862734618\n",
      "-----------------------------------\n",
      "CPU times: user 40 ms, sys: 4 ms, total: 44 ms\n",
      "Wall time: 40.7 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "limit_max = 1000      # right limit in the integration                \n",
    "call = S0 * Q1(k, cf_H_b_good, limit_max) - K * np.exp(-r*T) * Q2(k, cf_H_b_good, limit_max)\n",
    "print(\"Heston Fourier inversion call price: \", call)\n",
    "print(\"-----------------------------------\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "[1] Heston, S. L. (1993). \"A closed-form solution for options with stochastic volatility and applications to bond and currency options\". Review of Financial Studies\n",
    "\n",
    "[2] Schoutens, W., Simons, E., & Tistaert, J. (2004). \"A perfect calibration! Now what?\". Wilmott Magazine\n",
    "[link](https://perswww.kuleuven.be/~u0009713/ScSiTi03.pdf)\n",
    "\n",
    "[3] Yiran Cui, Sebastian del Baño Rollin, Guido Germano, (2017), \"Full and fast calibration of the Heston stochastic volatility model\" European Journal of operational research. [link](http://www0.cs.ucl.ac.uk/staff/g.germano/papers/EurJOperRes_2017.pdf)"
   ]
  }
 ],
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